Dealing with phase variability is crucial in functional data analysis.
Many different approaches exist for registering curves
[1]}, but their application to diverse real world data settings
remains challenging.
Most existing approaches target small to intermediate datasets of completely
observed curves with small amounts of Gaussian noise,
evaluated on dense, regular grids.
Especially the registration of incomplete curves, i.e., curves whose underlying process is
not observed from its natural starting point all the way to its natural endpoint,
has received only limited attention so far
, .
However, such data arise in many fields.
Missing information about the initial development of some
processes, i.e. leading incompleteness,
can be caused by different
starting conditions of subjects at the beginning of a study.
Trailing incompleteness towards the end of the
underlying processes is present in experiments and studies with a fixed endpoint that causes right-censoring,
or in panel studies with relevant dropout rates.
If both types of incompleteness are present, we use the term full incompleteness.
